prove that the bisector of two adjacent supplementory angles from a right angle

Asked by sbidipak | 27th Jun, 2017, 04:56: PM

Expert Answer:

begin mathsize 16px style angle DBA plus angle EAB equals 180 degree space space space space space space space CB comma space CA space are space bisectors space of space angle DBA comma space angle EAB space respectively
angle DBC equals angle CBA equals 1 half angle DBA......... left parenthesis straight i right parenthesis
angle EAC plus angle CAB equals 1 half angle EAB.. left parenthesis ii right parenthesis
angle DBA plus angle EAB equals 180 degree
Using space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
2 angle CBA plus 2 angle CAB equals 180 degree
angle CBA plus angle CAB equals 90 degree
In space increment BAC comma
angle BAC plus angle ACB plus angle ABC equals 180 degree
angle BAC plus 90 degree equals 180 degree
angle BAC equals 90 degree
the space bisectors space of space two space adjacent space supplementary space angles space include space straight a space right space angle.
end style

Answered by Sneha shidid | 27th Jun, 2017, 06:09: PM